What we know so far suggests the possibility that Cumberbatch wears part of a Starfleet uniform during some scenes in the movie only because it's given to him while held prisoner aboard the Enterprise. This would be like a number of characters in TOS, not limited to but including Khan.

John Harrison? The caption to the image is “(Left to right) Zachary Quinto is Spock, Benedict Cumberbatch is John Harrison and Chris Pine is Kirk in STAR TREK INTO DARKNESS from Paramount Pictures and Skydance Productions.” according to several sources. Are they trying to mess with us, or is this a new character not from canon? While its probably a red herring, someone at Superhero Hype pointed out both John Harrison and Gary Mitchell are 4-letter first names and 8-letter last names...

They're messing with us. Probably a lot of written material used in-house has substituted a fake name for the villain. Wouldn't be a complete shock if the name was used on call sheets, shot lists and even scripts.

Well, they've been trying to avoid telling who it is so far in all the trailers and previews.
So either someone at Paramount f'ed up and released the name or it's just something to throw the fans off and keep them guessing.

John Harrison? The caption to the image is “(Left to right) Zachary Quinto is Spock, Benedict Cumberbatch is John Harrison and Chris Pine is Kirk in STAR TREK INTO DARKNESS from Paramount Pictures and Skydance Productions.” according to several sources. Are they trying to mess with us, or is this a new character not from canon? While its probably a red herring, someone at Superhero Hype pointed out both John Harrison and Gary Mitchell are 4-letter first names and 8-letter last names...

Just for the hell of it I googled the name to see if anyone important ever had it. First result:

John Harrison (24 March 1693 – 24 March 1776) was a self-educated English carpenter and later a clockmaker. He invented the marine chronometer, a long-sought device in solving the problem of establishing the East-West position or longitude of a ship at sea, thus revolutionising and extending the possibility of safe long distance sea travel in the Age of Sail. The problem was considered so intractable that the British Parliament offered a prize of £20,000 (comparable to £2.87 million in modern currency) for the solution.[1][2]
Harrison came 39th in the BBC's 2002 public poll of the 100 Greatest Britons.[3]

"Harrison's name was mentioned in "Space Seed" and "The Naked Time". Harrison is one of only a few Starfleet personnel to wear the colors of all three TOS-era divisions (sciences blue, operations red and command gold) in his various onscreen appearances."